The 22-year-old has scored 15 goals in 22 appearances for Arsene Wenger's side this season as the Gunners sit at the top of the Premier League and are on course to secure qualification for the knockout stage of the Champions League.
"When you see what he is doing at the minute then why would you not say he is at a similar level [to Bale]?" Coleman told Sky Sports.
"What he's doing at the minute is enjoying his football. He's found his confidence again. He's always had the ability, he just needed to get the confidence back and he's got that.
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Coleman also praised Bale for his performances at Real Madrid and says that the winger, who has netted nine times in 13 appearances for Carlo Ancelotti's side, is beginning to find his rhythm after a start which was hampered by a thigh injury.
"He's proved everyone wrong again, including me," said the Wales manager. "I just thought any normal player who misses pre-season then it would take six months to get back and find your rhythm.
"A month ago after El Clasico he was getting criticised. Now, a month on, with more games, we are seeing his ability.
"He is proving he is a world-class player. If he was English or Spanish and producing those performances and then getting the move, I don't think much would have been said but, because he's Welsh and from a small footballing country, people have gone: 'Is he worth it?'
"Is anyone worth that money at the end of the day? But that is what someone has paid. It's not Gareth's fault but if we look at players all around the world and see what they can and can't do, there's not many that can do what Gareth does when he is at his best and he's finding that again. He's playing regularly and he looks fantastic."